Development a new thermodynamic model for aqueous polyelectrolyte solutions: extended UNIQUAC coupled with Manning's...

A comprehensive thermodynamic framework has been formulated to describe the behavior of aqueous polyelectrolyte solutions using the modified extended UNIQUAC approach. In the proposed model the short-range and long-range interactions have been modeled by the UNIQUAC and Debye-Hückel model, respectively. The effect of counterion condensation was accounted to estimate the effective charge density along the polyion backbone. Counterion condensation was incorporated to determine the reduced, effective linear charge density of the polyelectrolyte backbone. In addition, long-range Coulombic interactions were represented within the extended UNIQUAC model by introducing a Debye-Hückel term, which accounts for both polyion-counterion interactions and the electrostatic contributions arising from interactions among unbound counterions and added salt species. The developed thermodynamic framework was applied to calculate the osmotic coefficient and water activity of a series of aqueous polyelectrolyte solutions. These systems included sodium poly (acrylate) with degrees of polymerization of 5 and 15, ammonium poly (acrylate) with chain lengths of 5, 10, and 20, sodium poly (methacrylate) with polymerization degrees of 6 and 15, and sodium poly (2-acrylamido-2-methyl-1-propanesulfonate) with chain lengths of 2 and 10. The results demonstrate the model's capability to capture the thermodynamic behavior across different counterions, polymer backbones, and molecular weights. The model formulation explicitly incorporates temperature, polyelectrolyte molecular weight, linear charge density of the polyion, and electrolyte concentration as model variables. The model results indicate that the new approach provides reliable estimates of counterion activity coefficients in systems containing polyelectrolytes. For the seven systems studied, the average relative deviation was 4.59%, showing that the model gives accurate results. Because of its flexible structure, the model can be readily applied to new polyelectrolyte solutions that contain added salts in future work.